Something that I wanted to point out to people There there is a little better Of confusion at times on the strategy box and I wanna remind you of something that was said by to being the course I have my required concept formulas

00:25

And it's too nice pages and if you not as a very nicely does you basic definitions can be as large as the adjacent review them you're right I use the definition up in my strategy not ours said a definition if you use when his concept your use I use a definition up for Our impulse they are 2 main concepts for the course We are conservation of momentum in their on notice knew as laws you could always use of new insect laundering leaders does right I used in secular I used to Serb off death You're going to do something Like 1 of these 3 special cases where use the equation Leconte acceleration renews momentum countermeasure energy conservation these ones that you need to tell me why you use it and to use it For some these you better of told me your system so like energy conservation you better tell me system the same momentum conservation another set of 4 that but that it and then the a final list of a few miscellaneous definitions And use any of these ideas you exam use the definition of 1 of the following things so And of all these that the gravitational potential budget 2 bodies analog gravity to objects we get really use it maybe 1 homer can you read the section but you don't forget that this is that Right Every and these 2 shades of the class at really to shoot but you will use to solve the problems of final energy use and that these 2 should you will tell me your strategy that you use as simple as that Thank you could use short little phrases not big on competent every now and then look at disillusioned the 1 other like conceptual thing you will write I use the definition of static friction to check if it was a matter of right because you want tell me why you said it equals vs. less than people or something so there's a few other limited cases you want the solutions where there's 1 other thing in the strategy that I would say that it's almost always something from these 2 sheets and start of not only to shoot circuits that is very little And it's pretty obvious as you study you do want a review the strategy boxes that I wrote a check that led Iran strategy boxes from the surety Tech seated users not worried you go awry practice some problems using that that suggestion going forward any questions on that Excellent so now let's turn to actually jumped right into a problem

03:12

So we get on Wednesday basically some collisions or explosions where everything was in a line I wonder quickly do a case where maybe you have These components you can see what that looks like so worried take a bomb but Brynteg of all current throw wall notice and were throwing down at an angle 30 degrees The article so this says the incoming ball So this would be its initial momentum for either problem now I wrote the problem a little generically I say about the same speed and angle what is the average forced the ball out exactly 2 ways we can bounce off the same angle I can bounce back up at 30 degrees so this this case Water Iike imbalance Down at 30 degrees that be a relic a book us so this is 3 final in that case And this is P. final enacted what were asked about issues in both cases The force the average for some lot and we notice were given the time so we Amelia going to think of what It was That interactive Friday were you shout answers we really what it involves we think of involves because impulse is defined as a change in momentum but we also know It's caused by an average forest plans adopted and notice everything architecture is in terms of momentum and were asked the this and were given that so again except for the angle nature and the fact they were going angle this is basically that same sort of court not get a single step problem that would be thinking about practice Questions on a problem so I will come back to the clicker question but let's go right to the 1st version of it because the 1st version

05:59

I'm not asked as a clicker question but if Eurydice picket coordinate system here like a warning system would you work at Just the direction the ball's going right because everything's in a single line so there's no real we don't need XOY we don't need components we can just do this problem and we can take user I'm out of a warrant will be positive What I my noted that way to be positive and so what we see here this is final and this is the initial we negative initially equals P final and this statement true independent which way I picked my court system but that the basic Situation we have it's all in 1 direction and dealt the P is pretty easy right a GOP final minus P. initial and that's negative P final I just get to confine orders might answer and I was told it leaves with the same speed that it where And we're given the mass serve I look at all this the magnitude of dealt pity adjust to climb 0 . 1 kilograms Times 2 meters per 2nd so that's and v get . 4 Kilograms meters per 2nd and my direction is 30 degree is up to the left of the war so that really no different than wanted on Wednesday by 1 restore through that quickly any questions on that excellent so now I wanna aspect glitter questions a reader delicious draw grow quickly render the other version of it were comes in at 30 degrees and a goes out and 30 degrees our basic I gotta be asking do we want a standard cordon system like that or do we want what we just did Exulted cordon system like that but their basic question so let's vote on that day most we're going an angled pretty good so wire we going for an angle why would you pick this court system Why would that be a good court insist that Yes Guys so we might get to avoid doing component of but stock What I want you to do Right now right were were were really looking for Delta which means reading need perhaps a dealt PX quips At Delta P White And maybe by picking discordant system We're dog too much to back compliance embryonic get force 82 those directions By using that so quickly right down yourself what we Delta PXB what we Delta PYB will call this kinda show and this P final The reuse that Joked according Systempro 70 per cent of us pick to use that And just a Akerson said 30 degrees will tilt at that way so that's 30 degrees It everywhere OK it to Israel started suffer At the initial momentum is there any of it in a wide direction Yes how much data So this is all a P initial why what abandon the ax direction has that now for the final momentum how much is in a wider erection From Why would the ex directives are you all shock or be neighbor are y'all still show has anyone checked with this angle it went away anyone disturb now And if this 120 degrees is lined up with that now Right it's a that's an angle that so we have both PAY final and final because both components that That's not aligned along the x direction so it's a perfectly fine cornices and year truce but doesn't help you as much as you thought at the beginning right I think this every person and you pick that And hope that this would line up with that right But in fact it doesn't because In this particular problem the angle between the 2 is not 90 degrees because I'm having it come off at the 30 in the 30 them it said so in fact this problem is a little bit easier to do them I actually check this coordinate system map draws very well because they both have the same speed And there at the same angle so they have the the same light right there They have the same speed that we know the magnitude of the tour equal because the magnitude of envy final It was the bags of it and the initial because the math hasn't changed and the speed doesn't change that given that the same magnitude what you immediately from looking at us those of isometric thing And so what's true

12:57

About few final why as relations at peak initial White In the wider rights in their offices L There was going down one's going up But at a glance late In the wider racks but going down there so these tour he will West Road about Pete final why related I'm sorry I'm saying Why again P final act related the P initial acts Now they're able but opposite right so that is a negative so now what I have to say is the only change and he is the paedophile X minus the P initial acts and their equal and opposite so magnitude it's just 2 times the magnitude of initial acts as of now I just forgot brought in this case the extra but there's 30 this is the initial Signed 30 so I pick up that sign 30 and the change in Delta is now . 2 kilograms meters per 2nd and so the average forest is 20 new ends and it's been the negative x direction is 1 wagging given having defined quarters so comparing the that took greater force where's where's may have entered a greater force by Internet and of course but turned that indoor force its 40 new and takes twice the Florida turned the ball exactly around in this case But it does to does bouncer down in Assange beat Bonn yes now 1st any questions on that Now what we wanna moved to do so in this case notice we have what we call an ideal wall Friday nothing happened to wall of me in this case as a force of 20 villains and the ball went before summer Warsaw 20 million the other direction now the wall but in doing anything that originally task The Florin rigid wild and other forces acting on it so Giegerich free body diagram is no acceleration and so on and everything happened the ball now we want start way back collisions where both objects have things happen to them So the next day at the next for the chapter is to really focus on what happens in collisions and explosions And this organ a focus on both objects now right up to now we kind of have been taking the picture OK we have 2 of directing we know but Newton's laws there's an equal amount of force now report 1 object and see what happens to it so you can walk out launched refocused on the cannonball or the cannon And that's OK what happened because the polls his bothered along with voters around the ball because force it The wall and that imports now announced was the 2 objects as a single system and can we learn useful stuff there and that the number were the sort of 2 facts that we take into account what we do this 1 in 5 object any object B and they're going in Arak Where another Archer began what what what why am I holding up 3 fingers large others White They were complicit Right so I take this thing as a system right that we know Internal forces have no net impulse And we get pretty easily because of force food from BAT is the negative force on before many of the change in comment But a during this interaction as before Sunday Times delta T the change in momentum of being during this interaction is force on b during this time but this as it was minus the force a during this time so the total change momentum when I have to up to 0 not as fizzle out their friend how we might Think about forces in relation to the changes in energy were a comeback This is where we talk about He lasted vs. inelastic collisions 1 way out of between 2 objects We because we have different forms of energy we will often focus on 1 type of energy trader kinetic energy so you might get equal and opposite forces between the 2 objects but because kinetic energy doesn't worry about the signing right the total kinetic energy could change so simple case of this is a matter where I have An explosion right What's the kinetic energy before the explorers 0 that was an easy question was again and again after the explosion Large positive number right everybody's flying in different ways Everybody is squared nothing cancels out I did not serve kinetic energy of Forces involved changed whatever the energy source of the explosion was into kinetic energy now what about the momentum Was the momentum before The idea is you want velocities What's the moment it afterward past the Zero The title momentum still 0 so you can figure out where all the individual pieces when but wine you'll know where a lot because I know the momentum all others You know has that 0 you find the momentum the missing piece and you know where went so in a simple case of an explosion and the 2 pieces it's pretty easy to know where the other 1 went nowhere this 1 went so that's kind of a difference in collisions explosion between our momentum behaves energy because momentum as a actor and only as momentum energy is a scalar and different types

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Of energy so you think about them slightly differently the other thing that happens It is most of our collisions we will now they were focusing on the 2 object we really will think of them Instantaneous I really do an example in 2 seconds of a collision where 1 object is hanging on a pendulum the other object comes flying in and had And then they stick together and ask our route now divided roughly by this my system just these 2 objects or what everybody were doing it in the table so were near the Earth Draw your free body diagram for my sister of objects and the block doubt you've got a minute to draw free body diagram retract his speed testing for next week How many force is you have to what are they really are great weight down do we said we were merely Arthur was the other 1 Trenton out from this rather solving it So up during a collision do I have a change in momentum Possibly right Georgia which is bigger the tend to their however the nice thing is the change in momentum is before finds the time and if we assume a collision is instantaneous were assuming dealt is 0 so the change of momentum 0 so For most collisions that we will be looking at We will assume momentum is conserved assuming it's instantaneous now collision takes a long enough Then that will be true So I can add now I'm a really really slow Superman catching a really really slowly falling Lois Lane and take me a while they can share that acquires as were catching each other Gravity is still acting honors and removing sober you have to worry about that but at the typical speech Superman is traveling when Qatar mostly fight besides turning a new much ball when he gets on the collision itself was rather fast and we can pretty much ignore everything else does look at the collision is instantaneous and moment so 9 . 9 times out of 10 if there's a collision of problem unless I tell you how long the collision takes a asked you for the average force during the collision in which case to smoke Momentum impulse you will assume the collision saying 0 time and everything happens quickly and momentum to conserve Any questions on that Now of course Once that Collided in your here then my free body diagram comes into effect at the object move And they obey whatever at was MA laws replied that the final season collisions Will be what happens to the kinetic energy So this is just a quick little test Oh who read the book Britain and most garlic and this is what the NBA and the key areas with this idea of Elastic elastic Means exactly that we can serve a chemical energy all of our collisions pretty much at this point we just said will conserve momentum And there are going to be at the Delta T basically 0 and dealt at basically 0 that Time of space so we don't have to worry about those forces on the objects because of the do work change momentum after the collision takes place or but because now that being said what is mechanical energy They were remember other question right that was get theirs 3 examples of chemical energy that we have As a joy of 4 examples of energy formulas tree pretty theater 3 what are they ever test a week kinetic energy that the big where else sprang am was the other 1 Gravity so basically potential energy plus kinetic energy is your mechanical energy now that never happened often have problems with the collision that takes place on service friction Right I would As nice because frictionally dissipated over dozens date During that collision because we assume it happens in 1 spot your abroad effort so you have collision and then started moving in and out of The only time that's not true is if you have a collision with a big Spring between the 2 objects and what other colliding removes some distance D that the spring compressors and now run servers with and I've told you there will be no I have to worry about it and that it's trickier Basically the nice thing is most collision which are elastic they happen without a change in height NGH And very often does between 2 objects as no spring there and at the end of the day Again most of the time the mechanical engineer worried about his kinetic energy Looking at it would not allow that the reason is us is make Illinois On things deforming things a sticking together there's a lot of internal energy he and all that stuff and we talk about it as energy loss Eds But the one-time we get a little sloppy rule say how much energy was lost in the collision we really mean how much mechanical and who was lost right energy wasn't last adjusted to other types of energy sound He vibrations watching stuff but those all types of energy but they're not useful energy than I mechanical energy and so that's where we use that phrase any questions on that excellent so well But I want to do that now imagine we are now in your favorite crime show so you're either in CI CSI York Miami era where they were and CIS where you are the crime lab and you want to that you actually working the crime might well it in slightly olden days where this is a gun was the waterway but what are

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Asked to do The and some crimes shot a UN find the muzzle velocity of the bullet Coming out of the gun so often important factor of Identify with the boat may have come from what was going on now That's the board going leaves the gun at you know things about where got hit you user kinematics which in our expertise to you need all this work and serious Yes so you can see the practical we finally get the real practical stuff So what you did an activist has been done is Very rarely done for ballistic that's what we call ballistic pendulum by this the pendulum is designed so that shows that here they will stop Because then will ratchet that holds it place so goes out was a lover friction with that too much we get its maximum height again fall down more said So the bus That is also parcel of peace in Herald the Bulletin place so astute the bullet a Yoruba block They will go some height It'll start we would measure that height and that we could determine the speed at the boat left with At question so normally would safety goggles to ratify a bullet into a block away and then Asserted ended up about very exciting not Now there's a very good chance that if I repeat this I will break the apparatus but let me try quite member apparatus a script So did you missed the 1st time goes so fast pendulum at rest bullet at rest bullet fired The right now what I want you to do the obvious question

29:31

Where solve this problem Is to ask ourselves what type of visitors Sir go ahead and ask yourselves that and it so as before A argue that More than 1 of about about the show that now we have the obvious questions are a follow-up question It says it to the 380 or is it for me so God had an answer that sort for a large majority for 3 so given that we think it's 3 let process which is the obvious 1 that is in here Well that's the 1 Wicklow they have a collision in capturing the 2 Collide together right now once again worry about which 1 is obviously not in here and is not quite as obvious over about certain emotions poorly in here There's is now Reject a motion there's no point now you might say that would be all but reversed that right at the beginning here That's moving to grantee in others We purposely set up our device so the muzzle of the guide is right next to a block away So it leaves the garden goes right a block away so collision Nam I got going over here That I would or about what projectile margin wooden flying through the air under the influence of gravity and I have incorrectly so that I my block would ever when I my a block away but I would be going to be horizontal maybe going down mango cause I will falling So I eliminated projectile motion by setting it up very nicely so I go straight from a collision to what type of emotion as the pendulum doing circular credit cult because of you identified as reject emotions you might use your equation because acceleration weight Instead emerging do not apply so we had a circular motion We put it that that once again we have a tighter margin is not really relevant to a problem we have the explosion or watch But were not to worried has about what velocity does that leave the gun went Overnight asking about the involves the cause their velocity audacity of the force cause that Velocity world about what that velocity areas You know this is there we don't have to worry about it so again depending on how you look at the question as the same volley at last I thoroughly to way toward Labrador 3 of the problem They are so bones of mail Let's let's look at these and see how we might build on this problem

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Please Shares We've identified 2 lavish ends a Calais The Followed by Circular motion that want you like then applied The type of physics as well as a powerful technique then the tools you used to solve it Did much simplified once I have a collision now let me ask you this but do they stuck together beautifully Mechanical energy conserving this collision should be not anytime to stick together there is nothing else damage being done right the bullet to stick in the object proprietors stricter something something has happened a cause that stick whose energy associated the sticky any collision together are always Any elastic and the only thing you could do as cancer momentum so right away for Part 1 bit Only thing you learned in this class that will give you any Visitors information about their collision is momentum conservation so that the I have to use their momentum conservation as part of momentum impulse so you might be forgiven that way but you quickly get to Delta being 0 forces being 0 And The movie conserved with at 31 now circular motion part reactor got 2 routes that week What are the 2 things we can use for the circular motion part of the problem What we might find think in terms of the centripetal acceleration discord over our which would tell us There were using Newton's laws something with forces right these over we will use Newton's laws now with the other option when you and object were you know exactly what moves from an initial A final place member here it stops at the final height What's the other concept we would use for that type of situation energy now with amazed to is the 1 that is most That is best designed for dealing with initial and final and versus the wine but his best designed for dealing with things at a single time 1 of the 1st 2 words best that a single time from 1 of those too Works best for an initial and final which works best For a single time let's call take out your collectors that a bad which works best if you're considering behavior at a single incident time like 1 point in the circle the bottom of the circle the top of the circle the side of the circle 5 more seconds 3 June and 1 actually Farmers everybody went foreigners lost millions laws are things at tables and nite there's no before after just that single time energy conservation as what we focus on when we're doing in And the final so having taken the time to ask ourselves through reasonable question what motion do I observing the problem pick up the motion what physics plants that Go that motion lifted visits askance that you're now basically done with the problem right back is a I cannot know Why not comfortable with these kinds of your but this is Your Gault you wanna start thinking about these problems in this fashion past yourselves these questions visa Pavel questions that helped you get to the solution much faster than any other sort of Christ because your job on the final with these problems caesura Bob Lobel physics base to pick up those physics as quickly as you can again you're to shake summarize all of this which we learned Having our part 1 Botero their and our part to we can now proceed before we proceed any questions That can make sense we done this process twice that we did it Wednesday Committed to that So now let's look at it 1 week because our system because we're gonna do I concerning the bullet and the word that everybody diagram on that system we have the attention and the energy down but that's OK because were looking at a collision were dealt is basically 0 so I can conserve momentum so I'm going to do my before and my after that with conserving momentum when you make it charges of 80 again a user charges a couple Ediva ways to do it if you look at the Shiite I put up with a solution in this case I might do it as the ball at the words and the combined the 2 together

38:16

Because of the Show at what the momentum of the bullet and Italy The bullet initially 0 was all point of the problem defined next leader but Write it was fired and speed so will call that need not It is the initial momentum of the White the would be in a metal cylinder down there that 0 What's the combined momentum and initially but really just to add together or you can think of it as as not really relevant because not combined initially right at the end does not really exist all we have is the combined which is the Massimo bullet plus the mass of the word times the velocity of the 2 which I'm there called me so I was just starting out to go so Mike estimation momentum tells me that this is true so my I get from this man out as there will be some problems you did where you argument that now now you got right here is the symbol collision dealings collided alike to cars driving along and they had each other head-on and they stick together and this what was initially going 50 miles an hour with initially Aug 30 miles an hour with a speed when they're done you would have enough information to solve that problem is you have only 1 and everyone equation so a lot of these collisions of is just the collision You'll be done at this point unfortunately is not just the colors and suffer part Jr Right we now have our sister and where we have to be careful what a system for port A 3 objects in our system by we got our pendulum movie that order the 3 objects The bullet and the what their stuck together I want a 3rd object We are Who we want use potential energy of gravity right and we know that stirring circular motion so therefore the workers 0 and therefore we can conserve energy Rio work that so now we Merrill a table of initial and final really ever to energies kinetic and potential energy of gravity are initial is half the sum of the masses times via initial squared Our Finally 0 because stop we will take a gigolo 0 to be where the collision occurred The And then the final height Is H. R initial potential energy 0 our final is what is the sum of the 2 times G times H So as usual I would equate these 2 masses will cancel so I want the initial squared equals G H and that tells me and my initial it equals the square root of jujitsu and I can take that And I get it all away appear to be really messy and that maybe not that I got is MY as ever the bullet As an other word Over the mass of the ball at times a square root of 2 G 8 That I wanted to I could put in some numbers but that is basically all I need to do now the final question you might be asked and the 2 minutes without while you're packing up is how much energy is lost in the collision and barrier compare 1 And beat not square with 1 have NBA players MW the initials square and you'll see that this does not equal that Anders Energy lost necessary we will talk about on Monday colors